Affiliation:
1. Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg 620000, Russian Federation
Abstract
In this paper, we show that the nonlinear growth rate of particles in a supersaturated solution or supercooled melt, as well as the rate of removal of crystals from the metastable liquid of a crystallizer, significantly change the size-distribution function of crystals. Taking these rates into account, we present a complete analytical solution of the integro-differential model describing the transient nucleation of solid particles and their evolution in a metastable liquid. The distribution function and metastability degree (supersaturation or supercooling) are found by means of the separation of variables and saddle-point methods. The nonlinear growth rates of crystals in supersaturated solutions and supercooled melts (single-component and binary) are summarized and compared with experimental data.
This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.
Funder
Russian Science Foundation
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
54 articles.
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